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Math.signum() has been added to some of the mappings (Cos and Square) to better demonstrate their actual usage. If you want to use these two mappings, apply that first.
In order:
Red - Cos
Blue - Linear
Green - Cubic
Purple - Square
Black - Root (suspect that this is bugged, ignore)
z is the inputScale that is used by Root. It is unknown what z should be in an actual use case, so ignore z going from 1 to 5.
Linear is what is usually applied to joystick (no changes). The others apply minor changes that may be handy for some functions. Root is bugged and should be completely ignored.